cascade(hk, J=7)
The algorithm uses the vector cascade algorithm described by Strang and Nguyen in "Wavelets and Filter Banks". It builds a dictionary of values and slices for quick reuse. Then inserts vectors into final vector at the end.
Coefficients of low-pass filter.
Values will be computed at grid points K/2**J
. Default is 7.
The dyadic points K/2**J
for K=0...N * (2**J)-1
where len(hk) = len(gk) = N+1
.
The scaling function phi(x)
at x: phi(x) = sum(hk * phi(2x-k))
, where k is from 0 to N.
The wavelet function psi(x)
at x: phi(x) = sum(gk * phi(2x-k))
, where k is from 0 to N. psi
is only returned if :None:None:`gk` is not None.
Return (x, phi, psi) at dyadic points K/2**J
from filter coefficients.
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